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If you pick from each of the possible letters at each stage, then there are 5 possible options for the first letter. Then there are 4 possible options for the second. Then there are 3 possible options for the 3rd and so on. This leaves us with 5x4x3x2 = 120 different arrangements. However, each arrangement has been counted twice, as it doesn't matter which way around the Os go. So to get the true answer, we need to divide by 2. 120/2 = 60, and therefore the number of different arrangements of the letters in the word COLOR is 60.

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